## Hydrogen Atom Game Simulator Examples

### Energy Units

Energies in this game are given in electron volts (eV). This is a special unit used in atomic physics and chemistry and it is valuable because it saves the user from a lot of very small numbers. One electron volt equals 1.602 × 10-19 J. It is easy to convert between these two units.

For example, convert 4.56 eV to J.
```           1.602 × 10-19 J
4.56 eV · ---------------- = 7.31 × 10-19 J
1 eV
```
For example, convert 2.14 × 10-18 J to eV.
```                     1 eV
2.14 × 10-18 J · ---------------- = 13.3 eV
1.602 × 10-19 J
```

### Electron Energy Level Transitions

In this game an electron moves between energy levels, either absorbing or emitting energy in the form of a single photon. The energy of the photon matches the difference in the energies of two energy levels that the electron transitions between. To find the difference in energies just find the absolute value of the difference:

For example, say the electron transitions between level 7 and level 1. The difference in energies is then
|-13.606 eV – (-0.278 eV)| = 13.328 eV.

The energies given on the playing board are negative because they represent potential energy and when the electron is infinitely far away it has zero potential energy. As it gets closer to the nucleus the electron must lose energy (think of this as slowing down so it can be part of an atom). The energy values are negative because in order for the electron to get to that energy level it had to give up the amount of energy shown.

### Emission Card

The emission cards are the best to get because the team who gets one automatically gets to try for the points. Say the card you draw says to do a transition between energy level 7 and energy level 2. Place the electron marker on the playing board at 7 and move it to 2 to emit the photon. Fill in the first box and find the energy for that transition by subtracting:

#### Energy in Electron Volts (eV)

|-3.402 eV – (-0.278 eV)| = 3.124 eV
These results are always positive numbers. This answer tells you how much energy is carried by the single photon that is emitted by the atom when this transition takes place.

#### Energy in Joules (J)

Convert this value to joules (J) to fill in the second box on the scoresheet:
```            1.602 × 10-19 J
3.124 eV · ---------------- = 5.005 × 10-19 J
1 eV
```

#### Frequency in Hertz (Hz)

Find the frequency of the photon for this transition by using Planck’s Formula: E = hf. Remember, Planck’s constant (h) is equal to 6.626 × 10-34 J· s.
```           E   hf            E    5.005 × 10-19 J
E = hf     - = --    so  f = - = ---------------- = 7.554 × 1014 1/s (or Hz)
h   h             h    6.626 × 10-34 J· s
```

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#### Wavelength in Meters (m)

Find the wavelength of the light by using the Speed Formula: c = λf. Remember, c is the speed of light and is equal to 3.00 × 108 m/s.
```           c   λf            c    3.00 × 108 m/s
c = λf     - = --    so  λ = - = ---------------- = 3.97 × 10-7 m
f   f             f    7.554 × 1014 1/s
```

#### Wavelength in Nanometers (nm) or Micrometers (µm)

If the light emitted by the atom is in the visible or ultraviolet (UV) range then convert to nanometers (nm, 1 m = 1 × 109 nm). If the light emitted by the atom is in the infrared (IR) then convert to micrometers (µm, 1 m = 1 × 106 µm). This wavelength is in the visible region so the example shows conversion to nm.
```                 1 × 109 nm
3.97 × 10-7 m · ------------- = 397 nm
1 m
```

Now you have finished filling in the boxes for this turn on the score sheet. Mark the location of the spectral line on your spectra page for an additional point. If your calculations are all correct then you can earn a maximum of seven points. Compare your results with the opposing team’s to verify that your calculations are correct. Bring disputes to a referee or the teacher.

### Incoming Photon Card

Incoming photons bring in the element of chance. If you get an incoming photon card the electron on the playing board must be in the correct lower energy level in order for the light to be absorbed. Use the inventory of cards on the rule sheet to identify the transition intended by the card. You may only play the card if the energy shown on the card moves the electron from its current position to a higher energy level.

For example, say the card has the energy 2.551 eV. Find this energy on the rules sheet in the card inventory. The transition that this card allows when the atom absorbs a photon with this energy is from energy level 2 to energy level 4. Since the first example left the electron in energy level 2 on the playing board you can play this card.

If the card has the energy 13.328 eV then the transition is from energy level 1 to energy level 7. A photon with this energy can only be absorbed if it is already in the ground state (energy level 1). If the electron is in energy level 2 (or any other energy level) then the photon is not absorbed and the opposing team gets to draw a card.

All calculations from this point forward are exactly the same as for an Emission Card. Refer to the examples for each calculation above. The energy given on the card is what you place in the Energy (eV) column of the score sheet. Be sure to mark the spectra page to show the absorption line.

Rules of the Game
Rules for Referees
Score Sheet
Backs of Playing Cards
Playing Cards Page 1
Playing Cards Page 2
Playing Cards Page 3
Playing Cards Page 4
Hydrogen Atom Energy Level Diagram Playing Board
Emission and Absorption Spectra page
Last updated: Apr 26, 2009 Home